Question
Download Solution PDFयदि निर्देशांक अक्षों पर एक सीधी रेखा खंड का प्रक्षेप 6, 8, 0 हैं, तो खंड की लंबाई क्या होगी?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFसंकल्पना:
सदिश की दिशा कोज्या सदिश की लंबाई द्वारा सदिश के संगत निर्देशांक को विभाजित करने पर प्राप्त होती है।
यदि l, m, और n दिशा कोज्या हैं, तो l2 + m2 + n2 = 1
गणना:
निर्देशांक अक्ष पर सरल रेखा खण्ड का प्रक्षेप 6, 8, 0 है।
माना कि, l, m, और n दी गई रेखा की दिशा कोज्या है और सरल रेखा की लंबाई k है।
इस प्रकार, l = 6/k ⇒ lk = 6
m = 8/k ⇒ mk = 8
n = 0/k ⇒ nk = 0
अब,
\(\rm (lk)^2+(mk)^2+(nk)^2 =6^2+8^2 +0^2 \\ \Rightarrow (l^2+m^2+n^2)k^2=36+64+0 \\\Rightarrow (1)k^2=100\;\;\;\;\;(\because l^2+m^2+n^2=1) \\\Rightarrow k = 10\)
इसलिए, विकल्प (1) सही है।
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